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The local Langlands conjecture for \(\mathrm{GL}(p)\). (La conjecture de Langlands locale pour \(\mathrm{GL}(p)\).) (French) Zbl 0564.12020

Let \(F\) be a local field of residual characteristic \(p\). The note announces the existence of a Langlands correspondence between equivalence classes of p-dimensional semisimple representations of the Weil-Deligne group of \(F\) and irreducible admissible representations of \(\mathrm{GL}(p,F)\). The proof is sketched.
Almost the same work has been done by Ph. Kutzko and A. Moy, see their paper [Ann. Math. (2) 121, 495–517 (1985; Zbl 0609.12017)].
Reviewer: J. G. M. Mars

MSC:

11S37 Langlands-Weil conjectures, nonabelian class field theory
22E50 Representations of Lie and linear algebraic groups over local fields

Citations:

Zbl 0609.12017
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